第478回電波研連F分科会資料
開催日：2003年10月23日

UWB Indoor Propagation Channel Measurement– Based on Deterministic Approach –Katsuyuki Haneda, Jun-ichi Takada
Department of International Development Engineering
Tokyo Institute of Technology
2–12–1, O-okayama, Meguro-ku, Tokyo, Japan
Telephone, FAX: +81–3–5734–3288
Email: haneda@ap.ide.titech.ac.jp

Abstract— In this paper, a new Ultra Wideband (UWB) channel estimation algorithm, UWB-SAGE (Space Alternating Generalized Expectation Maximization) is proposed. In the algorithm, anovel UWB signal model which is an extention of the conventional
wideband signal model is employed in order to estimate the
UWB channel with SAGE algorithm. The algorithm divides
the measured data into individual ray paths and estimates the
directions of arrival, propagation time, and the variation of theamplitude and phase during the propagation for each signal. The
measurement campaign in indoor environment was conducted
and it was shown that the algorithm could correctly extract theinherent propagation phenomena of the channel. The estimation
result can be very useful for the design and analysis of UWB
communication system, especially for the evaluation of waveform
distortion and multipath effect.

I. I NTRODUCTION
Recent communication networks are required higher data
rate than ever and the UWB communication system has
drawn a lot of interests as a promising scheme to realize thisrequirement. In order to construct an efficient UWB system,
it is required to investigate the propagation channel where thesystem is to be implemented . Characterization of the channel
has been done by estimating the directions of arrival (DOAs)
and directions of departure (DODs) and the times of arrival(TOAs) of the waves from Tx to Rx. Channel modelling andclusterization of the potential scatterers are also important.
There have already been constructed theoretical and experimental schemes of channel sounding for wideband
channels[1], [2]. The measurement is often conducted by using
PN sequences and data processing is done in the frequency
domain. In the modelling of collected data, it is requiredthat the variation of transfer function within the consideredbandwidth B and antenna aperture A is sufficiently small,namely, a condition
A
(1)
B ¿1
c
must be held where c is light velocity. However, this condition
is not satisfied in UWB systems.
For UWB channel estimation, the use of Sensor-CLEAN
algorithm has been proposed [3], [4]. This algorithm estimates
not only DOAs and TOAs but also incident waveforms, thus
sequential data in time domain is necessary.

In this paper, we propose a frequency domain channelsounding scheme for UWB system, namely Ultra-Wide Bandwidth Space Alternating Generalized Expectation Maximization (UWB-SAGE) algorithm. In the algorithm, a novel UWB
signal model which is an extention of the conventional wideband signal model is employed in order to estimate the UWBchannel with SAGE algorithm. The SAGE algorithm has been
adopted for wideband channel estimation [5], [6]. In UWBSAGE, waveform estimation is not necessary because thealgorithm assumes the transmit waveforms to be known in
the receiver side and employs frequency domain processing.
The frequency domain measurement is easily implemented
with vector network analyzer and spatially scanning antenna[7] thus the algorithm is applicable for real environment
estimation. Note that the UWB communication is deployed
only for short range environment so that it is enough toconsider the network analyzer based system.
II. PATH M ODELIn the ray based propagation model which is applicablefor high frequency waves (also for UWB communication),
it can be defined that one propagation path has DOD, DOA
and TOA that does not depend on frequency, but has afrequency dependent complex gain. Herein a single directional
measurement model is considered i.e., DOD is not estimated,
hence the transfer function of one ray path yl (f, φl , θl , τl ) isexpressed asyl (f, φl , θl , τl ) = αl (f, τl )rl (f )D(f, φl , θl )

(2)

where
τl : propagation time,φl : arrival azimuth angle,• θl : arrival elevation angle,• αl (f, τl ) : complex gain of the spatial propagation,• rl (f ) : scattering loss,• D(f, φl , θl ) : radiation pattern of Rx antenna for a single
polarization.

••

Note that the gain of Tx antenna can not be modeled in
Eq. (2). Therefore, this effect is included in rl (f ) in thismodel. α(f, τ ) can be expressed as the extension of Friis’

Incident direction

For simplicity, we vectorize the data defined in Eq. (4) asyi

= [y1,1,1,i y2,1,1,i · · · yM1 ,1,1,i y1,2,1,i · · ·T=where M = M1 M2 M3 and ni is noise vector. si denotes atransfer function vector that is composed of propagation andantenna characteristics of each wave. Namely,

Scanning Plane  [deg] : Elevation angle,  [deg] : Azimuth angle
Fig. 1.

si

Definition of Angles at Rx

T

The multi-dimensional mode matrices Ai ∈ C M ×L is expressed as Eq. (10),1exp (−j2πτl f ).
4πτl f(3)

UWB-SAGE algorithm is based on the Maximum Likelihood Estimation (MLE) and has a high resolution in separating
the incident waves.

(2)

(1)

Ai = Ai (µi ) ¦ Ai (µi ) ¦ Ai (µi ),(3)III. UWB-SAGE A LGORITHM

A. The Data ModelT= [s1,i s2,i · · · sL,i ]= [α1 (fci , τ1 )r1 (fci )D(fci , φ1 , θ1 ), · · ·αL (fci , τL )rL (fci )D(fci , φL , θL )] ∈ C L . (9)Transmission Formula,αl (f, τl ) =yM1 ,M2 ,1,i y1,1,2,i · · · yM1 ,M2 ,M3 ,i ] ∈ C M
Ai si + ni ,
(8)

where
(r)

Ai (µi )(r)ai (µl,i )

h
iT
(r)
(r)
ai (µ1,i ) · · · ai (µL,i ) ,
h
i
(r)
(r) T
,
= 1 ejµl,i · · · ej(Mr −1)µl,i

=

(10)

(11)
(12)

and ¦ denotes the Kronecker product of each column of thematrices.
The UWB channel model can be derived as a simple I
superposition of this subband model.

Suppose that UWB channel can be expressed as the superposition of I subbands where the scattering loss and the B. SAGE Algorithm
antenna directivity within each subband is assumed to be
MLE estimates a component that maximize the likelihood
constant. When we focus on the ith subband whose center
function,
which is the probability of observing the measured
frequency is fci (1 ≤ i ≤ I), we can formulate a model
data
byassumingthat the data follows a certain distribution. In
of a measured transfer function. Suppose there are L waves
theconsideredsignalmodel, the received signal is perturbed
incident to uniform rectangular array (URA) in horizontalbygaussiannoise.
Therefore,
the probability of generating theplane which has equally spaced M1 , M2 antenna elements inmeasureddata
vectoryfromsignal component vector µi ,iazimuth and elevation directions. The azimuth and elevation
p(y
|µ
)
is
i
i
angles are defined as Fig. 1. The element spacings are ∆x and
M1 Y
M2 Y
M3 µ
∆y , respectively. By performing M3 frequency sweeping withY1
p(yi |µi ) =×
sampling interval ∆f at center frequency fci , the measured
πσk1 =1 k2 =1 k3 =1
transfer function yk1 ,k2 ,k3 is denoted as Eq. (4),·¸¶
|yk1 ,k2 ,k3 ,i − µk1 ,k2 ,k3 ,i |2
"
#
L
3
exp −
(13)
X
Y jk µ(r)σ2yk1 ,k2 ,k3 =αl (fci , τl )rl (fci )D(fci , φl , θl )e r l,iwhere the noise is assumed to be independent and identicallyr=1
l=1+nk1 ,k2 ,k3 .
(4) distributed.
By taking the logarithm, the maximum likelihood condition
where 0 ≤ kr ≤ Mr −1 (1 ≤ r ≤ 3) indicates a index number is expressed as the following minimization problem,of each sampling domain. nk1 ,k2 ,k3 is white gaussian noise of
1
(r)
min
||yi − Ai si ||2 .
arg max ln p(yi |µ) = 2 arg
zero mean. µl,i is expressed asµσ[φl ,θl ,τl ,sl ]L
l=1
(14)
2πf
ci
(1)
µl,i =∆x sin φl cos θl ,(5) The required search in Eq. (14) is a simultaneous 4L dimenc
sional one.
2πfci
(2)
To reduce the computationally prohibitive multidimensional∆y cos φl cos θl ,(6)
µl,i =
csimultaneous
search, the Expectation-Maximization (EM) al(3)µl,i = 2π∆f τl .
(7) gorithm is introduced [8]. This estimates the complete dataxl,i from the incomplete data yi as Eq. (15).
Plane wave approximation of the incident wave is used in thisformulation.
xl,i = al,i sl,i + βl,i (yi − Ai si )(15)Herein the nature of the additive white gaussian noise isconsidered in the derivation and the initial values of theparameters are needed. βl,i is a positive number which has aPLconstraint l=1 βl,i = 1 but is practically set to 1. This makes
us possible to maximize the conditional Fisher information ofcomplete data xl,i [6]. In our case, incomplete data means themeasured data and complete data corresponds to the data ofeach incident waves which are not directly measured in theexperiment. The modified log-likelihood function for complete
data is analogous to Eq. (14),arg max p(xl,i |µ) = arg min ||xl,i − ai si ||2 .
µ[φ,θ,τ,s](16)This means that the simultaneous search dimension is reduced
to 4. We can see that the search estimates the parameters of
the waves which extract the largest power from the complete
data. Thus, we can rewrite this minimization procedure in thefollowing 3-dimensional simultaneous search.
(φ̂l , θ̂l , τ̂l ) = arg max | z(φ, θ, τ, xl,i ) |[φ,θ,τ ](17)

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Residual Data

Measured Data



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H
NOQPSRV TQU Z O
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Global Search
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  Set
"!#%$&(' )+*8 9:;< :;"=#:;%>&:(? @+A

As Initial Values
Local SearchFindz y {| } y {"~ Simultaneously

Find

 

Find

 

The cost function z(φ, θ, τ, xl,i ) is denoted asz(φ, θ, τ, xl,i ) = E[aHi xl,i ].

(18)

This is equivalent to finding the matched filter for a certain
incident wave. The complex transfer function of the wave sl,iis derived from the estimated parameters as,z(φ̂l , θ̂l , τ̂l , xl,i ),(19)M
and the path gain Pl,i = |sl,i |2 is obtained.
SAGE algorithm divides the whole search space of EM
algorithm into hidden data spaces. In our case, the search iscarried out sequentially in the following order,

Yes

Convergence
Achieved ?

Noa^"`b_ a ced f _ Resulta c(d g _ a ced h _ a cXi jXk a c lKm
Fig. 2. Flow chart of the SAGE algorithm of SIC type for each subband [9].

sl,i =

φ̂l= arg max | z(φ, θl , τl , xl,i ) |,

(20)

θ̂l

=

arg max | z(φ̂l , θ, τl , xl,i ) |,

(21)

τ̂l

=

arg max | z(φ̂l , θ̂l , τ, xl,i ) | .

(22)

φ
θ

τ

In this way, we can obtain updated estimates of parametersfrom the old ones. This process is repeated until the likelihood
reaches a certain maximum value or the estimated parametersconverge on some fixed value.
C. UWB-SAGE Algorithm
As explained in section III-A, UWB channel can be
expressed as a set of subbands. Therefore, in the UWBchannel estimation, the cost function to be maximizedz(φ, θ, τ, {xl,i }Ii=1 ) is a simple summation of modified loglikelihood of each subband as Eq. (23).
z(φ, θ, τ, {xl,i }Ii=1 ) =

I
X
¯
¯
¯E[aH
¯
i xl,i ]

(23)

i=1

In the use of SAGE algorithm, SIC (Successive Interference
Cancellation) type procedure is preferable when the numberof samples is sufficiently large [7], [9]. An example of thesearch procedure is depicted in Fig. 2. This scheme is acombination of local search based on SAGE algorithm andglobal mesh search based on EM algorithm. In global meshsearch, we aim at the region which may include a maximum
point of the cost function. After that, local search is carriedout inside the selected region to find an accurate peak. The
process is repeated until the number of detected paths reaches
the predefined number of waves or the detected path level
falls below the noise floor level. The transfer function of ith
subband channel is obtained from Eq. (19).
It should be pointed out that the system parameters to be
optimized in the estimation are the following two, which must
be adjusted within the criteria of Eq. (1):1) Sampling interval of frequency domain ∆f .
∆f gives the upper bound of arrival time without the1
appearance of aliasing, τmax =.
∆f2) The number of samples in spatial domain M1 , M2 andin frequency domain M3 I.
These parameters decide the basic resolution of thealgorithm.
IV. UWB C HANNEL M EASUREMENT
A. Measurement System and Environment
With the UWB-SAGE algorithm and measurement system
proposed in [7], we estimated typical indoor channel with

Receiver Antenna( Biconical )Transimitter Antenna( Biconical )TABLE IS PECIFICATIONS OF THE M EASUREMENT

X-Y Positioner(DEVICE D3425AV1/O-D)

Cable (6m)Cable (20m)and Controller(DEVICE DX3165AV1/O-C)

Network Analyzer( Agilent 8720ES )Preamp (30 dB)

Port1

Port2

Measurement ofSetting
position

751 points (∆f = 10 [MHz]).
800 [MHz]In horizontal plane, 10 × 10 points ofrectangular array configuration whose
intervals are 4.8 [cm](less than half
wavelength in 3.1 [GHz])
Azimuth φ, elevation θ,
propagation time τ and variation ofspectrum in terms of phase and gain.
Biconical antennas for Tx and Rx.
100 [Hz].

The number of samples
in spatial domain

Cable (0.5m)

GPIB

3.1 [GHz] ∼ 10.6 [GHz][10]Bandwidth considered
The number of samples
in frequency domain
Bandwidth ofeach subband

GPIB

Estimated components
Note PC
Control and data acquisition
Signal Processing

UWB channel measurement system.

Floor to ceiling : 2.6m
Wall (c)Path #1, 3
Path #4

4.33m
Scanning Plane

Vertical–Vertical.
−98 [dBm].
10 [deg] for azimuth or elevation,
0.2 [ns] in time domain.
Back-to-back, the distance between
Tx and Rx is 0.7 [m].

Calibration
Wall (d)Rx(h: 0.70m)

Wall (b)6.67m

Path #5

Path #6Tx(h:1.58m)
Path #2

Wall (a)7.67m

Fig. 4.
Floor plan of the measurement environment and result of path
identification.

-50
Friis’ transmission formula
Measured data

-55
Amplitude [dB]Fig. 3.

Antennas
IF Bandwidth
Polarization of
the wave
Noise level of
network analyzer
Resolution of
UWB-SAGE algorithm

-60
-65
-70
-75
4

UWB signal in order to assess the validity. Figure 3 is thearchitecture of the measurement system. The system measures
the transfer function by Vector Network Analyzer (VNA) andthe synthesyzed antenna aperture is achieved with one element
antenna and spatial scanner.
The floor plan of the measurement environment is depicted
in Fig.4. The Tx and Rx antennas are set in the same room withdifferent height. The size of the room is about 6.7 × 7.7 [m2 ]and are typical small conference room. There is almost no
objects in the room except for the measurement equipment.
During the experiment, the door was closed so that the channel
was considered to be time invariant. The specifications of
the measurement and UWB-SAGE algorithm implementation
are listed in Table I. Note that the back-to-back calibration
is a simplified procedure which removes the mismatch loss
occured between cables and antennas. In the case of executing
this procedure, it should be satisfied that only the direct pathexists. Therefore, in the on-site calibration as our experiment,
we used the electromagnetic absorber so as to isolate the Tx
and Rx antennas from objects surrounded.

5

6
7
8
Frequency [GHz]910

Fig. 5. Measured power spectrum and the Friis’s free space transmission
formula.

B. Results
Figure 5 is the averaged power spectrum obtained from
VNA. The free space gain of direct wave derived from Friis’
transmission formula [11] is also shown. They have small
difference and it is assumed that the direct component isdominant in this line-of-sight environment. The fluctuation of
the measured power spectrum is due to the multipath effect.
The results of parameters estimation with UWB-SAGE
algorithm is shown in Table II. There are 6 waves detected
including direct path and reflected rays from each side of thewalls. In the table, parameters derived from geometical optics
method (GO) are shown as well and they agree well withthe estimated ones. This means that all the waves are almost
identical to the specular reflected paths. For all the paths, we
can see some deviation between the estimated result and theone derived by the GO. In angle domain, this kind of error

-57

R ESULT OF PARAMETERS ESTIMATION BY UWB-SAGE-58

ALGORITHM

-59

Path
identification#1
Direct wave
#2
Wall(a) rflct.
#3
Ceiling rflct.
#4
Wall(b) rflct.
#5
Wall(c) rflct.
#6
Wall(d) rflct.

Azimuth[deg]
359.30(0.00)
303.70(302.04)358.90(0.00)
180.90(180.00)
61.60(56.00)359.70(0.00)

Elevation
[deg]
13.80
(11.49)13.80(6.15)
29.90(34.00)13.40(5.25)
15.40(6.48)
11.3(8.07)

Delay
[ns]
15.30
(14.73)
29.03(27.37)
18.63(17.40)34.70(32.03)29.86(25.98)21.49(20.91)

Amplitude [dB]TABLE II

-60
-61
-62
-63
-64
-65
4

5

6
7
8
Frequency [GHz]

9

10

4

5

6
7
8
Frequency [GHz]

9

10

-5
-10
-15

is due to the worse accuracy of endfire direction estimation.
On the other hand, phase characteristics of the antennas could
cause a bias on the delay estimation, although the effect is not
significant.
The estimated gain and phase of direct path are depicted inFig. 6. The phase shown in the figure indicates the deviationfrom the free space phase variation, namely in this case, thephase rotation at antennas. For the reflected waves, the phasecomponent obtained in the estimation includes both antennas
and reflection (scattering) phase characteristics.
V. C ONCLUSION
We proposed an algorithm which estimates the UWB
propagation channel in a deterministic way, named UWBSAGE. This algorithm employs the novel UWB signal model
which is an extension of conventional wideband signal modeland conducts a frequency domain processing, therefore theestimation of time domain waveforms is not required. The
indoor channel measurement suggested that the algorithm
could correctly separate the incident waves and evaluate theparameters of each wave.
In the processing of UWB-SAGE, antenna directivity is
regarded as isotropic because of the difficulty of embedding
them into multi-dimensional mode matrix Ai in Eq. (8).
Therefore, the estimation results include both characteristics
of antenna and propagation. For the spectrum, propagation
characteristics can be extracted from the estimated result
by deconvoluting the effect of antenna directivity and its
frequency dependence.
We must assess our algorithm in several aspect, for example,
experimental velification of the resolution. The behavior of
the algorithm for the estimation of waves whose delays andangles are much closer compared to the resolution is also of
the interest. At the same time, several measurements not only
in LOS but also in NLOS environments are needed for theaim of UWB channel modelling.
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-35
-40
-45
-50
-55

Fig. 6.

Estimated amplitude and phase of direct wave.

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